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arXiv · 1509.01681

Characterization of stadium-like domains via boundary value problems for the infinity Laplacian

Graziano Crasta·Ilaria Fragalà
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Abstract

We give a complete characterization, as "stadium-like domains", of convex subsets $Ω$ of $\mathbb{R}^n$ where a solution exists to Serrin-type overdetermined boundary value problems in which the operator is either the infinity Laplacian or its normalized version. In case of the not-normalized operator, our results extend those obtained in a previous work, where the problem was solved under some geometrical restrictions on $Ω$. In case of the normalized operator, we also show that stadium-like domains are precisely the unique convex sets in $\mathbb{R}^n$ where the solution to a Dirichlet problem is of class $C^{1,1} (Ω)$.

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Graziano Crasta, Ilaria Fragalà. 2015-09-05. Characterization of stadium-like domains via boundary value problems for the infinity Laplacian. https://doi.org/10.1016/j.na.2015.12.007

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